The debate about the future ownership of Royal Bank of Scotland was kickstarted on Wednesday just hours before the bank was slapped with a fine for rigging Libor.

As recently as a year ago, Vince Cable had been arguing for full nationalisation of the bank in which the taxpayer owns 82% of the shares. An early draft of a speech the business secretary was to deliver on Wednesday revived the idea of handing shares to the public, first mooted by the Liberal Democrats in 2011, although the speech he delivered called more generally for "all options" to be considered.

His concern about RBS, he told the Guardian, was that the bank is in the "worst of all worlds, where we're responsible but we don't have control where we can direct it".

There are a range of options:

• Do nothing

Sit on the shares in RBS, currently trading around 341p, until UK Financial Investments, which looks after the shares for the taxpayer, can start to sell them off at a profit. According to Cable such a possibility is "a distant dream".

To complicate matters, RBS has rejigged its share price from the bailout so that the average price at which taxpayers bought is 500p, rather than the 50p originally. The average is based on three tranches of shares.

Some 22.8bn were bought in December 2008 at a price of 65.5p (now 655p); the second was a preference share conversion in April 2009 when 16.7bn shares were bought at 31.75p (317.5p) and then a further slice in December 2009 of 51bn shares at a price of 50p (500p). There has been talk in the past of the first tranche of shares being sold off at a loss but above the lowest in-price of 317p. UKFI has sounded out wealthy Middle Eastern investors to buy up tranches of shares.

• Nationalise the bank

Cable admits that he wanted to take full control of RBS during the crisis and has argued since then that nationalising the bank might be one way to bolster business lending. But he admits that this would cost too much money at a time when the government's purse is shut tight – even when the governor of the Bank of England has been calling on banks to raise more funds from their shareholders.

• Mutualisation

The Liberal Democrat MP Stephen Williams was a behind a plan, devised by Portman Capital Partners, to hand out shares to all 46m adults on the electoral register. The idea is that each person would receive about 1,450 shares in RBS (before the share consolidation or 145 aftewards) and 440 in Lloyds Banking Group, into which the taxpayer pumped £20bn and owns just under 40%. By guaranteeing a fixed nominal amount to the Treasury when the shares are sold, through setting a "floor price", the government would recoup the £66bn it pumped into the banks.

• Split it up

The independent commission on banking, chaired by Sir John Vickers, called for a ringfence to be erected between high-street banks and investment banks, of which RBS has a large operation. One idea could be to go further than this and split RBS up along its high-street banking arm – perhaps renamed after NatWest, the bank it bought in 2000 - and its investment banking business.